NEW YORK CITY — Negotiations between union workers and the Con Edison utility company broke down Sunday morning in the midst of a heat wave blanketing the city. Con Edison has closed walk-in centers and limited work on major construction projects as a result of the breakdown in negotiations.

A spokesman for the Utility Workers of America said the 8,500 unionized workers told the company they would be willing to work without a contract to keep the power running, recognizing the city’s weather problems. In response, Con Ed said it offered a two-week extension of the current contract while negotiations continued but it was not signed.